The 2013 Australian Graduate Survey found that 71.3% of all Australian resident bachelor degree graduates had found fulltime work within four months of completing their degrees. Now imagine that a researcher carries out a follow-up study by surveying a representative sample of 1,000 recent graduates and finds that 72.1% have found full-time work within four months of completing their degrees.

a. At the 0.01 level of significance, can you state that more than 71.3% of new graduates are finding full-time work within four months of completing their degrees?

b. At the 0.05 level of significance, can you state that the proportion of new graduates who have found full-time work within four months of completion has changed since 2013?

c. What conditions needed to be met in order to answer parts (a) and (b)?